Question

Two charges of $40\mu C$ and $90\mu C$ are placed at a distance of $1\text{m}$ from each other. Where should a third charge be placed on the line joining them, if total force on the third charge is zero?

• A. In between, $40\text{cm}$ from $90\mu C$
• B. In between, $40\text{cm}$ from $40\mu C$
• C. In between, $50\text{cm}$ from $40\mu C$
• D. In between, $20\text{cm}$ from $90\mu C$

Answer 1

The correct option is B In between, $40\text{cm}$ from $40\mu C$


Here, $l=1\text{m}$
Net force on charge $q=0$
$\Rightarrow k\frac{(40\times {10}^{-6})q}{x^2}=\frac{k(90\times {10}^{-6})\times q}{(1-x{)}^2}$
$\Rightarrow 4(1-x{)}^2=9x^2$
$\Rightarrow x=\frac{2}{5}\text{m}=40\text{cm}$